Recovering singularities of a potential from singularities of scattering data

In this paper we show that the leading singularities of certain potentials can be determined from the leading singularities of the backscattering (as well as other determined sets of scattering data). The potentials in question are conormal with respect to smooth surfaces of arbitrary dimension; the restrictions on their orders allow for unbounded potentials in all dimension greater than or equal to three.Partially supported by NSF Grant DMS-9101298 and an Alfred P. Sloan Research FellowshipPartially supported by NSF Grant DMS-9100178     

Resonance scattering and singularities of the scattering function

Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such singularities produce a significant effect upon the pole behaviour of the scattering matrix, and more significantly upon the associated residues. This mechanism explains why by proper choice of the system parameters the resonance cross section is increased drastically in one channel and suppressed in the other channel.     

From superradiant Rayleigh scattering to Bragg scattering

We present the results of an experiment on light scattering from an elongated Bose-Einstein condensate interacting with far off resonant laser light. Due to superradiant Rayleigh scattering a coherent superposition of two atomic wavepackets with different momenta forms in the presence of a single laser beam. Varying the intensity of a weak counterpropagating laser beam we observe the transition from the pure superradiant regime to the Bragg scattering regime, where Rabi oscillations in a two-level system are observed. The process is limited by the decoherence between the two atomic wavepackets.     

On the compensation of bound and scattering state contributions to the partition function

The well-known compensation between bound and scattering state contributions to the hydrogenic partition function is studied for general potential forms, in the WKB approximation.     

S-Matrix singularities in scattering of charged particles on hydrogen-like targets

The scattering of a charged particle on an excited degenerate state of a hydrogen-like system is considered. The threshold and angular singularities of binary scattering amplitudes in this problem are studied. For these singularities closed-form analytical representations are obtained.     

High-energy scattering in QCD and cross singularities of Wilson loops

We consider elastic quark-quark scattering at high energy and fixed transferred momentum. Performing factorization of soft-gluon exchanges into the Wilson-line expectation value we find that there is one-to-one correspondence between high-energy asymptotics in QCD and renormalization properties of the so-called cross singularities of the Wilson lines. Using this relation we show that the asymptotic behavior of the quark-quark scattering amplitude is controlled by a 2 × 2 matrix of the cross anomalous dimensions. We evaluate the matrix of the cross anomalous dimension to two-loop order and study the properties of the obtained expressions to higher loop order.     

Singularities and accumulation of singularities of πN scattering amplitudes

It is demonstrated that for the isospin I = 1/2 πN scattering amplitude, T^I=1/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ and $s={m}_{N}^{2}+2{m}_{\pi }^{2}$ are two accumulation points of poles on the second sheet of complex s plane, and are hence accumulation of singularities of T^I=1/2(s, t). For T^I=3/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ is the accumulation point of poles on the second sheet of the complex s plane. The proof is valid up to all orders of chiral expansions.     

Three-body scattering at positive energies: Solving the problem of moving logarithmic singularities

For three-body scattering at positive total energies, integral equations are obtained whose kernels have no logarithmic singularities on the contour of integration. The corresponding singularities that are present in original integral equations can be circumvented by shifting a part of the contour of integration from the real axis to the complex plane. This is done only for a special auxiliary solution appearing to be an analytic function in this region. The physical amplitude proper is found as one of the solutions to the resulting set of equations. In contrast to conventional techniques, an additional analysis is therefore not required here, so that numerical solutions can be obtained within standard computational schemes.     

The physical meaning of scattering matrix singularities in coupled-channel formalisms⋆

The physical meaning of bare and dressed scattering matrix singularities has been investigated. Special attention has been attributed to the role of the well-known invariance of the scattering matrix with respect to the field transformation of the effective Lagrangian. Examples of evaluating bare and dressed quantities in various models are given.     

Quantum scattering in the strip: From ballistic to localized regimes

Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined. Received: 28 January 1998 / Revised: 16 June 1998 / Accepted: 6 July 1998     

高斯相关随机表面光散射散斑场相位奇异及其特性的理论研究

通过对二维高斯相关随机表面在远场平面上产生的散斑场及其相位的计算模拟, 发现在某一平面上除了实部零值线与虚部零值线有传统相交之外, 还有相切和重合的情况.切点和重合线也可以形成相位奇异, 并且其周围相位分布与传统的实部零值线与虚部零值线相交形成的奇点周围相位的螺旋变化不同, 呈现出对称性和不连续性的特征. 随着光波的传播, 在不同的观察面上散斑场复振幅的实部零值线和虚部零值线的相对位置经历了由相切到重合再到相交的演变过程, 相位奇异现象也随之发生变化. 关键词： 相位奇异 相位跃变 散斑场     

From jets to colour portraits of hard scattering final states

An original method for constructing parton final states emphasising the multi-element antenna pattern and colour connectedness between partons is presented. The approach should allow event-by-event reconstruction of parton final states from detector registered particles while avoiding the ad hoc effects of a jet algorithm. This strategy connecting soft hadrons to a set of partons rather than jets is demonstrated for -events and is applicable to W pair, top quark, Higgs, etc., production. Received: 12 May 1998 / Revised version: 5 June 1998 / Published online: 8 September 1998     

From 4d superconformal indices to 3d partition functions

An exact formula for partition functions in 3d field theories was recently suggested by Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific q-hypergeometric integrals whose key building block is the double sine function (or the hyperbolic gamma function). Elliptic hypergeometric integrals, discovered by the second author, define 4d superconformal indices. Using their reduction to the hyperbolic level, we describe a general scheme of reducing 4d superconformal indices to 3d partition functions which imply an efficient way of getting 3dN=2 supersymmetric dualities for both SYM and CS theories from the “parent” 4dN=1 dualities for SYM theories. As an example, we consider explicitly the duality pattern for 3dN=2 SYM and CS theories with SP(2N) gauge group with the antisymmetric tensor matter.     

Mean of the singularities of a Gibbs measure

We calculate the value of teh average of the singularities of a Gibbs measure invariant with respect to an expansiveC ² diffeomorphism of a one-compact manifold. This is the value related to dimension that one computes numerically. We then define and study a function, known as the correlation dimension, which is related to a free energy function, and we generalize the results in higher dimension with an axiomA transformation acting on a two-compact manifold.     

Metamaterial-based source and scattering enhancements: From microwave to optical frequencies

A brief review of metamaterial applications to source and scattering problems in the microwave and optical frequency regimes is given. Issues associated with modelling these systems are discussed. Electrically small radiating and scattering systems are emphasized. Single negative, double negative, and zero-index versions of these metamaterial-based systems are introduced that provide a means to manipulate their efficiency, bandwidth, and directivity characteristics.     

OddC gluonic regge singularities of perturbative QCD and their decoupling from deep inelastic neutrino scattering

The QCD motivated integral equation for three reggeised gluons in the oddC colour singlet channel is solved for large external masses of gluons. It generates a Regge singularity forj?1. Possible contribution of this singularity to the “non-singlet” structure functionxF ₃ is examined atx?0, where in principle it should give a constant term and dominate over the valence quark contribution. The coupling of the three gluon system to currents is, however, shown to vanish in the lowest order and in higher orders in the multi-Regge approximation.     

Scattering contributions to the internal partition function of a diatomic molecular system

An analytical expression for the phase shift contribution to the internal partition function for the Morse potential is derived by using an approximate Jost function. This function is shown to be a convergent sum. The numerical results obtained for H₂ and HCl show the partition function to be a monotonically increasing function of temperature. This observation agrees with the results of Rogers and co-workers. Work supported in part by the Department of Atomic Energy, Government of India.     

Fermi-edge singularities in AlxGa1-xAs quantum wells: extrinsic versus many-body scattering processes

A Fano resonance mechanism is evidenced to control the formation of optical Fermi-edge singularities in multisubband systems such as remotely doped AlxGa1-xAs heterostructures. Using Fano parameters, we probe the physical nature of the interaction between Fermi sea electrons and empty conduction subbands. We show that processes of extrinsic origin like alloy disorder prevail easily at 2D over multiple diffusions from charged valence holes expected by many-body scenarios.